Its hard to say.
From GSP's perspective, of course there are benefits and harms of moving up to fight Silva.
By moving up to fight Silva, he stands a chance of snatching the GOAT status from Silva. I believe that the aim of every fighter is to become the best of all time. If GSP gets past Condit, it probably is the best time for him to fight Silva. GSP is in the prime of his career, while Silva might be starting to go downhill ( although he still wins in darn spectacular fashion ). A win over Silva would be amazing for GSP's career. He beat the man much larger than himself, the man who dominated middleweights and some light heavyweights. He would be an even bigger PPV draw than he already is. His salary would shoot through the roof, and there would be some major sponsors looking for him.
Furthermore, if he loses, many would brush it off saying he is just too small for Silva, or he lost to the best there ever was. Really a win-win situation for GSP. If he wins, he is quite clearly the best of all time. If he loses...well there ain't no shame in losing to Anderson Silva. GSP could just move back to welterweight and dominate, or wait for Silva to retire so he can rule the middleweight division. I believe people would respect GSP more if he seeks to challenge himself and fight Anderson Silva instead of getting decision wins over welterweights that are quite clearly below him in terms of skill.
However, although GSP has nothing to lose in terms of legacy, money wise it is a different matter. It would be harder for GSP to ask for a better contract should he lose a fight against Anderson Silva. Also, less sponsors would be interested in GSP. They would much rather flock to the guy that won, Anderson Silva. He might also lose some fair-weather fans.
As for UFC, I don't think it is really wise for them to put up the fight. You have a dominant welterweight champion and dominant middleweight champion that are two of the biggest draws in the company. You put them against each other and one of them is definitely going to be less of a draw. If GSP loses, you can't really promote him as the GOAT after Silva retires. Silva might retire after winning GSP, and what good would it do for the business? If Silva loses, it kind of devalues the middleweight title. Your middleweight champion who absolutely ruled the division lost to a...welterweight. That is of course if the bout happens at catchweight. If GSP moves up to middleweight permanently then it would be fine.
Fans want to see the fight, yes. UFC would appease all the hardcore fans if the fight happened. However, I don't think UFC would have any less PPV buyers if the fight DIDN'T happen. They would get to earn big numbers for...one PPV. After that, if Silva retires after winning, you have one of your top draws retire while another top draw loses some fans for losing. Just not a wise business decision for the UFC.
Of course, I'm not a businessman so I might not be entirely right.
Silva would dominate GSP.
Edit: 5a.m here, mind not really functioning right yet...might comment more later on.